The melody for Happy Birthday is copyrighted and not due to expire until 2030.  It is currently owned by Warner Brothers which earns more than $2 million USD per year, through enforcing its rights via ASCAP. 

Here is the long and the short of it, if you sing Happy Birthday to your family and a few friends at home; you're probably have not committed any copyright infringement. However, if you perform that same tune in a bar, restaurant or club - and if the restaurant doesn't have an agreement to pay ASACP fees, you maybe engaging in copyright infringement.

It is unclear from my research as to who changed the lyrics to from "Good Morning to All" to "Happy Birthday". 

Note:  Too many friends and you maybe engaging in copyright infringement.  Warner Brothers seriously and agressively enforces their claim for ASCAP fees on Happy Birthday.  The United States copyright law in United States Code, defines publicly performing a work as "to perform or display it at a place open to the public or at any place where a substantial number of persons outside of a normal circle of a family and its social acquaintances is gathered."  They also sell the sheet music for $3.95 a crack over 115 years after it was first published.